Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9y5)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-39/8, b>=a

For fixed z and a=-39/8, b=-9/8

http://functions.wolfram.com/07.23.03.b9y5.01

Input Form

Hypergeometric2F1[-(39/8), -(9/8), 11/2, z] == (1/(48601700268825 z^(9/2))) (1024 (-4 Sqrt[z] (-79856 + 1190710 z - 9138521 z^2 + 53999768 z^3 - 12320937153 z^4 - 13148805996 z^5 - 724484235 z^6 + 76895472 z^7 - 8269611 z^8 + 495726 z^9) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((1277696 - 19929776 z + 159209335 z^2 - 963007746 z^3 + 7867328273 z^4 + 10194397164 z^5 - 14483344191 z^6 - 3047717010 z^7 + 323873247 z^8 - 34069896 z^9 + 1982904 z^10) Sin[ArcSin[Sqrt[z]]/4])))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]